**FACTORISING A QUADRATIC MEANS PUTTING INTO 2 BRACKETS**

1.** ** THE STANDARD FORMAT FOR A QUADRATIC EQUATION IS: ax² + bx + c e.g x² + 3x + 2 = 0²

**2. ** **FACTORISING METHOD WHEN “****a=1”**

**3. ** **ALWAYS REARRANGE INTO THE STANDARD FORMAT:** **“ax² + bx + c = 0”**

**4. ** **WRITE DOWN THE** **2 BRACKETS** **WITH THE** **x’s IN: (x )(x )=0**

**5. ** **THEN FIND** **2 NUMBERS** **THAT** **MULTIPY** **TO GIVE** **“c”** **BUT ALSO** **ADD/SUBTRACT** **TO GIVE** **“b”**

**6. ** **PUT THEM IN THE BRACKETS AND CHECK THAT THE** **SIGNS** **WORK PROPERLY OTHERWISE YOU WILL GET THE WRONG ANSWER**

**7. ** **TO CHECK YOUR ANSWER EXPAND THE** **2 BRACKETS** **TO SEE IF YOU HAVE MATCHING ANSWERS TO THE QUADRATIC EQUATION!**

**WHEN a DOES NOT =1**

**E.G SOLVE 3x² + 7x=6 BY FACTORISING**

**1. ** **REARRANGE IT TO THE** **STANDARD FORMAT**

**2. ** **THEN BECAUSE** **a = 3** **THE** **2 x** **TERMS WILL HAVE TO MULTIPLY TO GIVE** **3x² SO THE BRACKETS WILL BE: (3x )(x )=0**

**3. ** **NOW LOOK AT ALL THE** **PAIRS OF NUMBERS** **THAT WILL** **MULTIPLY** **WITH EACH OTHER TO GIVE** **c** **AND** **ADD/SUBTRACT** **TO GIVE** **b** **SO EITHER** **1 X 6** **OR** **2 X 3**

**4. ** **NOW TRY** **ALL THE POSSIBILITIES** **IN THE BRACKETS AND** **ELIMINATE** **WHICH EVER ONES YOU** **DON’T NEED.**

**5. ** **(3x 1)(x 6)** **multiplies to give** **18x** **&** **1x** **which also add/subtract to give** **17x or 19x**

**6. ** **(3x 6)(X 1)** **multiplies to give** **3x** **&** **6x** **which also add/subtract to give** **9x or 3x**

**7. ** **(3x 3)(x 2)** **multiplies to give** **6x** **&** **3x** **which also add/subtract to give** 9x or 3x

8. **(3x 2)(x 3)** **multiplies to give** **9x** **&** **2x** **which also add/subtract to give** 11x 0r 7x

9.** ** So (3x 2)(x 3) is the combination that gives b=7

**10. ** **Now fill in the** **+/-** **signs so that the combination adds up to** **+7** **so that brackets are** **(3x - 2)(x + 3)**

**11. ** **To check** **expand** **the brackets to see if you end up with the** **original equation!**

** HOPE THIS HELPS:D**

Answered Tue 31st May, 2011 @ 23:05 by

SONIKA